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CIE
2010
Springer

Computable Ordered Abelian Groups and Fields

10 years 1 days ago
Computable Ordered Abelian Groups and Fields
Abstract. We present transformations of linearly ordered sets into ordered abelian groups and ordered fields. We study effective properties of the transformations. In particular, we show that a linear order L has a 0 2 copy if and only if the corresponding ordered group (ordered field) has a computable copy. We apply these codings to study the effective categoricity of linear ordered groups and fields. Key words: computable algebra, effective categoricity. We study complexity of isomorphisms between computable copies of ordered abelian groups and fields1 . Recall that an ordered abelian group is one in which the order is compatible with the additive group operation. Ordered fields are defined in a similar manner. We say that an ordered abelian group A = (A; +, ) is computable if its domain A, the operation +, and the relation are computable. Similarly, a field is computable if its domain and its basic operations are computable. If A is computable and isomorphic to B, we say that A is ...
Alexander G. Melnikov
Added 06 Dec 2010
Updated 06 Dec 2010
Type Conference
Year 2010
Where CIE
Authors Alexander G. Melnikov
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